# Equivalence Classes

#### iwish123

Hello, Im having problems with equivalence classes.

The relation R is defined for complex numbers z=x+yi and w=a+bi. zRw if and only if x+b=y+a

I am asked to give the elements of the equivalence class containg

I have wrote, ={xeC:xRi}={xeC:x-i} to begin finding the equivalence classes, but am stuck trying to find the elements

#### Plato

MHF Helper
Is this true $$\displaystyle (0+1\cdot i)\mathcal{R}(1+0\cdot i)?$$

#### iwish123

No, because you can't relate the real numbers to the imaginery numbers?

#### Plato

MHF Helper
No, because you can't relate the real numbers to the imaginery numbers?
What are imaginary numbers?
Are they ghosts of dearly departed real numbers?

#### iwish123

What are imaginary numbers?
Are they ghosts of dearly departed real numbers?
The real numbers are a subset of the complex numbers. a+ib is a complex numbers, so imaginary numbers can be added or subtracted to the realnumber to form a complex number.

I know i^2 is -1

So the equivalence class containing i will just be those elements congruent to i? So the elements would be the complex numbers. Or is this chasing the wrong argument?